On double bound graphs and forbidden subposets

For a poset P=(X,⩽P), the double bound graph (DB-graph) of P is the graph DB(P)=(X,EDB(P)), where xy∈EDB(P) if and only if x≠y and there exists n,m∈X such that n⩽Px,y⩽Pm. We show some characterizations on split double bound graphs, threshold double bound graphs and difference double bound graphs in terms of (n,m)-subposets and double canonical posets.